A freight train of constant speed v and length L must cross a river that is spanned by a single straight bridge of length D. For safety reasons the entire train must be on the bridge before any section of track on either shore can bear its weight.
Neglect any changes in speed during the crossing.
(1) Using a point-mass model for the train, determine the time required for the train to cross the bridge.
(2) Using the actual length L of the train, determine the correct time required for the entire train to clear the bridge.
(3) Derive an algebraic expression for the ratio of the times found in parts (a) and (b).
(4) If L≪D, evaluate the ratio obtained in part (c) to leading order and interpret physically why the point-mass approximation becomes acceptable in that limit.